−143231
Explanation:The general term of a geometric series can be described by the formula:
an=arn−1
where the initial term is a and common ratio r.
Then we find:
(1−r)N∑n=1an=N∑n=1arn−1−rN∑n=1arn−1=a+N∑n=2arn−1−N∑n=2arn−1−arN=a(1−rN)So dividing both ends by (1−r) we find:
N∑n=1an=a(1−rN)1−r
In our example, N=7, a=−11 and r=−5
So:
7∑n=1(−11)(−5)n−1=
